An undistorted α-helix architecture displays backbone azimuthal rotational angles (Ω) of 100° (Eq. (S1))27. Over this helical scaffold, the side chains of periodically repeated amino acids (i, i + x) generate a family of helical topologies on the surface of the α-helix. The projection angle established between consecutive side chains of the exo-helical pattern can be defined as the exo-helical torsion angle (χ) (Fig. 1A). This χ angle is solely dependent on Ω and the number of residues (x) in the pattern (i, i + x) as defined by Eq. (S2). Thus, χ values for every possible pattern constitute a distribution of even angles separated by 20° when displayed in a helical wheel with full rotation at (i, i + 18) (χ = 0°, Fig. 1A). Positive χ angles —right half of the helical wheel— describe right-handed (P) helices, whereas negative χ—left half of the helical wheel—define left-handed (M) helices (Fig. 1A). All resulting exo-helices can be conveniently grouped in helical symmetry families as shown in the χ vs. rise (Δ) plot (Fig. 1B). Apart from χ, exo-helical pitch (P), Δ, and number of monomers per turn (N) are needed to precisely define each exo-helix (Fig. 1C, see (i, i + 1)).All geometrical parameters can be calculated for any repetition pattern by simple equations (Eqs. (S3)–(5) and SI Table 1). The possible exo-helices can be predicted by the general helical symmetry model7. In this model, a helical symmetry group originates when the number of amino acids from a repetition pattern (x) is a prime number (Fig. 1B, C, SI Table 1, and SI Fig. 1). Exo-helices generated when x is a composite number are included in their related prime symmetry—e.g., exo-helices formed by (i, i + 3) and (i, i + 6) patterns are both included in the same helical symmetry (Fig. 1B and SI Fig. 1). However, when χ exceeds half rotation in the helical wheel (χ > 180° or χ < −180°, Fig. 1A), a secondary helical symmetry group is induced —e.g. exo-helix generated by (i, i + 4) with respect to (i, i + 2) (Fig. 1B, and SI Fig. 1).Exo-helices included in the first seven group symmetries claim our attention since they have the smallest Δ values and are possibly the most relevant examples (Fig. 1C). 2/1 (i, i + 9) and 1/1 (i, i + 18) symmetries corresponding with χ angles of 180 and 360°, respectively, both lead to the non-helicoidal (lineal) topology. +18/5 is the origin symmetry that contains the non-prime/non-composite repetition pattern (i, i + 1) and describes an exo-helix with the same structural characteristics as the α-helical backbone (Fig. 1C). Every single exo-helix can be unequivocally expressed by the formula ±R/T, where (±) defines the right (+, P) or left (−, M) handed helical sense, R indicates the total number of helical monomer repeats per turn, and T the total number of turns (Fig. 1C). The first prime repetition pattern (i, i + 2) describes an -9/4 M-helix with an exo-helical rotational angle of −160°. Due to this short pitch (0.68 nm), this prime pattern originates a singularity. As the i ↔ i + 4 exo-helical residues are closer in space than i ↔ i + 2—Cβ–Cβ distance of 5.7 vs. 7.7 nm, respectively— thus, the (i, i + 2) pattern gives rise to a double exo-helical topology formed by two homologous (i, i + 4) P-helices within the symmetry group +9/1 (Fig. 1C). The repetition patterns (i, i + 3) and (i, i + 6) originate to two analogous M-helices: the −6/1 and the −3/1, respectively, the latter having a half number of monomers per turn (N = 3) and double exo-helical rotational angle (χ = −120°) (Fig. 1C). The prime number repetition pattern (i, i + 5) draws a unique +18/7 exo-helix with P chirality (Fig. 1C). Finally, the (i, i + 7) pattern defines a −18/1 M-exo-helix with a long helical pitch and the shortest possible rotational angle between repeated side chains (χ = −20°, Fig. 1C).The observation of the non-canonical exo-helical peptide topologies has been typically hindered, in part due to the complex structural analysis of peptides in solution. An undistorted α-helical peptide scaffold, together with a suitable characterization technique, are both required. In this sense, circular dichroism (CD) continues to be one of the techniques of choice for the determination of the average peptide secondary structure in solution due to its simplicity and versatility28. Thus, we designed a series of peptides that allow the characterization of the different exo-helices by CD spectroscopy. An oligo(glutamic acid) was selected as the backbone since this sequence folds into a highly stable helical conformation when protonated29. The low molar attenuation coefficients of the aromatic chromophores in proteinogenic amino acids (i.e., Phe, Tyr, and Trp) and their significant overlap with the amide in the UV–Vis absorbance spectrum preclude their application in the spectroscopic characterization of the exo-helices30. Therefore, 7-nitro-1,2,3-benzoxadiazole (NBD) was selected as a suitable chromophore for the spectroscopic characterization of the exo-helical topologies produced by the first repetition patterns (i, i + x; x = 2–7). NBD has a much stronger absorbance with maxima at 482 and 348 nm (S0 → S1 and S0 → S3 electronic transitions, respectively), which do not overlap with the amide UV trace31,32. In addition, the relatively small molecular size of the NBD allows multiple functionalizations of the peptide backbone without significant helix perturbation33.Molecular dynamic (MD) simulations of all the NBD-bearing peptide sequences (SI Table 2) were first carried out to estimate the average structural parameters. Root-mean-square deviation (RMSD) analysis of 2 ms long trajectories showed stable structures for all peptides, which supported the calculated trajectories as representative examples of the corresponding experimental spectroscopic traces. The averaged structures and centers of mass of the individual NBD moieties were obtained considering the whole trajectory. We could observe that the calculated azimuthal angle of the protonated oligoglutamic backbone was close to 100° (Ω = 99.0° ± 0.3), which confirmed an ideal α-helical folding in all cases. Four parameters defining all exo-helices were extracted from each averaged structure: (i) distance between neighboring NBDs (d), (ii) radius of the exo-helix formed by NBD moieties (r), (iii) helical pitch of the exo-helix (P), and finally (iv) exo-helical rotational angle (χ) as the projection angle of the chromophores’ centers of mass (Fig. 2 and SI Table 3).Fig. 2: CD spectra and MD simulated averaged structures of the first six patterns (x = 2–7).For all sequences (M-helices: A 7KNBD, B 3KNBD, and C 6KNBD top row; P-helices: D 5KNBD, E 4KNBD, and F 2KNBD bottom row): CD and UV–Vis spectra (top box). Zenithal and lateral views of the superposition of the structures in the trajectory of the MD simulation (one structure every 500 ns, backbone is represented as a gray cartoon and KNBD residues in color shades (bottom-left box). Zenithal and lateral views of the MD simulation averaged structure and the NBD centers of mass together with the exo-helical representation (bottom-right box). Structural parameters of the exo-helix (χ, r, P, and d) from the averaged structure are denoted. The calculated rotational angle of the oligo(glutamic acid) backbone (Ω) was close to the ideal value (99°), confirming the correct folding of the calculated α-helix core for all cases. θBB and θNBD expressed in deg × cm2 × dmol−1. εBB and εNBD expressed in cm2 × dmol−1.Oligo(glutamic acid) based peptide scaffolds were synthesized through Fmoc solid-phase strategy. Orthogonally protected side chains of lysines—i.e., methyltrityl or allyloxycarbonyl protecting groups—were installed at the NBD targeted positions of the repetition patterns (i, i + x) (SI section 5). N-terminal acetylation and C-amidation were used to enhance peptide folding into α-helix and avoid undesired interhelical aggregation. Chromophore insertion was performed on resin by selective deprotection of the orthogonal group followed by nucleophilic aromatic substitution using NBD-Cl as electrophile. All targeted NBD-peptide sequences were obtained in high purity after HPLC purification (SI section 6). UV–Vis and CD spectroscopy data of peptide solutions (~50 μM) were recorded using 2,2,2-trifluoroethanol (TFE) as a solvent to ensure the correct folding of the individual helices (SI Table 5, SI Fig. 9–14)34,35. CD spectra were expressed in two molar ellipticities (θ) depending on the chromophore absorption range and normalized to the number of chromophores (eq. S8): (i) one for the peptide backbone (θBB, 190–260 nm) considering the total number of amides and (ii) a second one for the exo-helix region (θNBD, 260-600 nm) considering the number of NBD moieties. The CD signal intensity in the amide region and signal intensity ratios at the two characteristic minima (222/208 nm) experimentally confirmed the nearly ideal α-helical conformation (~80% helical content) for all peptides studied (SI Table 5). Potential chiral induction interferences between α-helix backbone and the NBD were discarded with a single NBD labeled control peptide (SI Fig. 9 and SI Table 3).As described by the model (Fig. 1), the three-dimensional arrangement of NBD lateral residues defines a rotation sense —P (+) or M (−)— for each exo-helix. MD simulations outlined left-handed exo-helices for 7KNBD (i, i + 7), 3KNBD (i, i + 3), and 6KNBD (i, i + 6) patterns (Fig. 2A–C). The corresponding CD traces of these three patterns revealed a negative to positive exciton coupling corresponding to the NBD S0 → S1 transition (≈460 nm). A less intense positive signal could also be observed from the S0 → S3 NBD transition (≈330 nm). Thus, this CD footprint was assigned to the M exo-helix generated by NBD chromophores. In detail, the M-exo-helix defined by 7KNBD confirmed the predicted exo-helical rotational angle with a slight deviation (χ7 = −31.8°, Fig. 2A). This exo-helix displays the NBD moieties in relatively close spatial proximity (d7 = 1.1 nm), which results in a strong NBD exciton signal (Fig. 2A). The low torsional angle and tight packing of side chains of this helical topology is optimal for the establishment of side-to-side interactions between α-helices19,36. Since the other two M-patterns (6KNBD and 3KNBD) belong to the same helical symmetry group (1C3), they describe equivalent M-exo-helices with identical helical pitch (Fig. 2B and C). However, 6KNBD contains half the chromophores per helical turn than 3KNBD, conferring a higher rotational degree of freedom to the chromophore moieties (Fig. 2B and C). The increased rotational freedom, together with the predicted longer interchromophore distance, is reflected in the lower exciton coupling intensity of 6KNBD when compared to 3KNBD.As predicted by the model, repetition patterns 5KNBD (i, i + 5) and 4KNBD (i, i + 4) showed stable right-handed exo-helices in their MD simulations, which are experimentally confirmed by the NBD exciton couplings signature inversion (positive to negative) (Fig. 2D and E). For 5KNBD, as anticipated from its long average inter-NBD distance (d5 = 1.6 nm), only a weak bathochromic exciton coupling was observable (Fig. 2D). 4KNBD also describes a P-exo-helix with an exo-helical rotational angle of 34.8° and a helical pitch of 6.1 nm (Fig. 2E). The average interchromophore distance for 4KNBD (d4 = 0.8 nm) is the shortest of all investigated patterns —as could be expected due to the anatomy of the α-helix with hydrogen bonds between (i, i + 4) residues. Therefore, this pattern shows the highest intensity of the CD trace for the NBD S0 → S1 transition. The more energetic transition S0 → S3 is also sensitive to the macrochirality of the exo-helix showing a positive to negative exciton coupling. The effect of the short distance between chromophores in 4KNBD can also be confirmed by the blue shift of the absorbance maximum in the UV–Vis spectra (Fig. 2 and SI Fig. 15C).2KNBD average structure analysis confirms a significantly larger interchromophore distance i ↔ i + 2 (d2 = 1.7 nm) when compared with four amino acids separation i ↔ i + 4 (d4 = 0.8 nm) (Fig. 2F). As previously mentioned, considering these distances in the exciton coupling theory, the (i, i + 4) contribution in the CD spectra will be predominant over that of the (i, i + 2) pattern. Thus, 2KNBD will be experimentally observed in CD as an exciton coupling corresponding to two (i, i + 4) helices, which could be confirmed by the observed positive to negative (S0 → S1) exciton coupling (Fig. 2E and F). The slight decrease in the CD intensity of the 2KNBD in comparison to 4KNBD can be explained by the higher rotational degree of freedom of four terminal chromophores instead of two (Fig. 2E and F). Interestingly, the S0 → S3 NBD transition has a transition dipole moment (tdm) perpendicular to S0 → S1 that is more sensitive to the (i, i + 2) exo-helix M-chirality and thus displays the expected negative to positive exciton coupling.To understand the influence of the lateral chain molecular size in the exo-helix persistency, we next stepwise reduced the alkyl chain connecting the NBD moiety with the α amino acid from l-lysine (K, 4xCH2) to l-ornithine (O, 3xCH2), l-2,4-diaminobutyric acid (B, 2xCH2), and finally l-2,3-diaminopropionic acid (X, 1xCH2). The shortening of the alkyl linker directly reduces the rotational degree of freedom of the NBDs, which affects interchromophore distance and NBD’s tdm orientation persistency (Fig. 3 and SI Table 3)37. Since the exciton coupling intensity is directly dependent on these parameters, CD spectroscopy should accurately report on the impact of the linker length in the exo-helix spatial distribution38.Fig. 3: Influence of the linker length (K (CH2)4, O (CH2)3, B (CH2)2, and X CH2) in the interchromophore distance and transition dipole moment orientation and its observation in CD and UV–Vis spectra for the (i, i + 4) repetition pattern.Exo-helical radii (r), interchromophore distance (d), and transition dipolar moment deviation angles (β1 and β2) represented in the MD simulation averaged structure output of 4KNBD (A), 4ONBD (B), 4BNBD (C), and 4XNBD (D). Interchromophore distance (d) (E), root mean square of the β1 and β2 standard deviations (RMSσβ) (F), wavelength for NBD S0 → S1 transition maxima in UV–Vis (G), and CD NBD exciton coupling intensity at 485 nm (H) versus linker length. CD maxima expressed in deg × cm2 × dmol−1.The different repetition patterns (i, i + x) of the O, B, and X peptide series was thus simulated in MD experiments, synthesized, and characterized (UV–Vis, CD) analogously to the K series (SI Figs. 9–14). For all these new peptide series, the structural values of the backbone (222/208 ratio, and % α-helix in TFE) were comparable to the K series (SI table 5). The CD spectra revealed, in all cases, the same signs as the K patterns in the NBD exciton coupling, confirming the existence of similar exo-helixes in the new three series (Fig. 3A–C and SI Figs. 10–14). In the X series, the NBD’s most energetic band at 230 nm overlaps with the 222 nm signal of the peptide bond, thus influencing the 222/208 ratio. The (i, i + 4) pattern can be used to exemplify the different structural (MD) and spectroscopic (CD) implications of the alkyl linker length reduction (Fig. 3). Shortening the linker length linearly reduced the average interchromophore distance (d) and increased the orientation persistency of the NBD S0 → S1 tdm (Fig. 3A–F). Considering that the orientation of the individual (S0 → S1) NBD transition dipole moments start at the NBD center of mass and are directed towards the nitrogen atom of the nitro group (red arrows in Fig. 3A–D). The chromophore’s tdm orientation persistency was measured by comparing the variations of the tdm projections in the zenithal (β1 angle) and lateral (β2 angle) planes (Fig. 3A–F). Thus, the root mean square of the averaged β1 and β2 standard deviations (RMSσβ) was considered to parametrize the relative chromophore orientation persistency (Fig. 3F). A high RMSσβ value was observed for the 4ONBD, which can be rationalized by the potential promiscuous interactions established between the NNBD-H and the glutamic acid carboxylate groups, which are located at the closest distance in the ornithine linker. Following the expected trend, the shortest linker (X) showed the highest orientation persistency. This is supported by the favorable hydrogen bond formation between the NNBD-H donors and the carbonyl acceptors of the peptide backbone (NNBD-H…O = C(i+4)) (SI Fig. 16).As dictated by the exciton coupling theory, the effect of the chromophore to backbone distance will directly influence the two above-mentioned factors and, consequently, the UV–Vis and CD traces6. Consistently, we could observe the hypsochromic shift of the UV-Vis maxima, being the 4XNBD the most blue-shifted due to the shortening of d (Fig. 3G). On the other hand, the CD trace is more sensitive to the magnetic field, as can be observed from the exponential increase of the NBD exciton coupling intensity with the chromophore orientation persistency (Fig. 3H). This trend was observed for all repetition patterns (SI Fig. 15), with the shortest linker (X series) being in all cases the most persistent in the tdm orientation and CD signal, thereby precisely matching the proposed topological model. Therefore, this observation confirms that the persistency of the exo-helix is dependent on the degree of freedom of the lateral chain. This linker length and the possible interactions of the exo-chiral pendant with the α-helix backbone can enhance the stability of certain conformations of the chromophore pendant, which will then influence the exo-helix spatial persistency. Naturally, the strength of exo-helical interactions and the function of these chiral topologies will be related to this persistence.In conclusion, we introduce and experimentally demonstrate a general model for the exo-helical topologies of the α-helix secondary structure. A collection of oligo(glutamic acid) peptide scaffolds equipped with NBD chromophores at patterned positions were designed, simulated, synthesized, and spectroscopically characterized. The different repetition patterns (i, i + x) showed CD exciton couplings that consistently correlated in sign and intensity with the structural characteristics of the predicted exo-helices and their MD-simulated averaged structures. Spectroscopic elucidation of the topological model by varying the exo-helical linker length precisely matched the interchromophore distances and chromophore orientation persistency calculated by MD simulations with the exciton coupling theory. The chiral model herein proposed and spectroscopically validated confirms the α-helix potential to define different exo-helical chiral symmetries through repetition patterns in the amino acid sequence. At the present time, the future applications of the here-described exo-chiral model of the α-helix remain to be explored. However, the exo-chiral topologies of the α-helix have the potential to open the design of peptide non-canonical assemblies with multiple low-energy states, which can be found in certain functional proteins39,40. Moreover, we foresee that analogous exo-helical frameworks will be possible for any other helical peptide motifs, such as the 310 helix, the π-helix, and related foldamers. In addition, we expect that the exo-helical model of the α-helix will assist in the future design of non-canonical folding motifs, the synthesis of homochiral peptide replicators, and the development of new stimuli-responsive helical polymers and biocompatible sensors of chirality.
